VideoPoet is a large language model developed by Google Research in 2023 for video making. It can be asked to animate still images. The model accepts text, images, and videos as inputs, with a program to add feature for any input to any format generated content. VideoPoet was publicly announced on December 19, 2023. It uses an autoregressive language model.
Aldus PhotoStyler
Aldus PhotoStyler was a graphics software program developed by the Taiwanese company Ulead. Released in June 1991 as the first 24 bit image editor for Windows, it was bought the same year by the Aldus Prepress group. Its main competition was Adobe Photoshop. Version 2.0 (late 1993) introduced a new user interface and improved color calibration. PhotoStyler SE - lacking some features of the version 2.0 - was bundled with scanners like HP ScanJet. The product disappeared from the Adobe product line after Adobe acquired Aldus in 1994.
Flajolet–Martin algorithm
The Flajolet–Martin algorithm is an algorithm for approximating the number of distinct elements in a stream with a single pass and space-consumption logarithmic in the maximal number of possible distinct elements in the stream (the count-distinct problem). The algorithm was introduced by Philippe Flajolet and G. Nigel Martin in their 1984 article "Probabilistic Counting Algorithms for Data Base Applications". Later it has been refined in "LogLog counting of large cardinalities" by Marianne Durand and Philippe Flajolet, and "HyperLogLog: The analysis of a near-optimal cardinality estimation algorithm" by Philippe Flajolet et al. In their 2010 article "An optimal algorithm for the distinct elements problem", Daniel M. Kane, Jelani Nelson and David P. Woodruff give an improved algorithm, which uses nearly optimal space and has optimal O(1) update and reporting times. == The algorithm == Assume that we are given a hash function h a s h ( x ) {\displaystyle \mathrm {hash} (x)} that maps input x {\displaystyle x} to integers in the range [ 0 ; 2 L − 1 ] {\displaystyle [0;2^{L}-1]} , and where the outputs are sufficiently uniformly distributed. Note that the set of integers from 0 to 2 L − 1 {\displaystyle 2^{L}-1} corresponds to the set of binary strings of length L {\displaystyle L} . For any non-negative integer y {\displaystyle y} , define b i t ( y , k ) {\displaystyle \mathrm {bit} (y,k)} to be the k {\displaystyle k} -th bit in the binary representation of y {\displaystyle y} , such that: y = ∑ k ≥ 0 b i t ( y , k ) 2 k . {\displaystyle y=\sum _{k\geq 0}\mathrm {bit} (y,k)2^{k}.} We then define a function ρ ( y ) {\displaystyle \rho (y)} that outputs the position of the least-significant set bit in the binary representation of y {\displaystyle y} , and L {\displaystyle L} if no such set bit can be found as all bits are zero: ρ ( y ) = { min { k ≥ 0 ∣ b i t ( y , k ) ≠ 0 } y > 0 L y = 0 {\displaystyle \rho (y)={\begin{cases}\min\{k\geq 0\mid \mathrm {bit} (y,k)\neq 0\}&y>0\\L&y=0\end{cases}}} Note that with the above definition we are using 0-indexing for the positions, starting from the least significant bit. For example, ρ ( 13 ) = ρ ( 1101 2 ) = 0 {\displaystyle \rho (13)=\rho (1101_{2})=0} , since the least significant bit is a 1 (0th position), and ρ ( 8 ) = ρ ( 1000 2 ) = 3 {\displaystyle \rho (8)=\rho (1000_{2})=3} , since the least significant set bit is at the 3rd position. At this point, note that under the assumption that the output of our hash function is uniformly distributed, then the probability of observing a hash output ending with 2 k {\displaystyle 2^{k}} (a one, followed by k {\displaystyle k} zeroes) is 2 − ( k + 1 ) {\displaystyle 2^{-(k+1)}} , since this corresponds to flipping k {\displaystyle k} heads and then a tail with a fair coin. Now the Flajolet–Martin algorithm for estimating the cardinality of a multiset M {\displaystyle M} is as follows: Initialize a bit-vector BITMAP to be of length L {\displaystyle L} and contain all 0s. For each element x {\displaystyle x} in M {\displaystyle M} : Calculate the index i = ρ ( h a s h ( x ) ) {\displaystyle i=\rho (\mathrm {hash} (x))} . Set B I T M A P [ i ] = 1 {\displaystyle \mathrm {BITMAP} [i]=1} . Let R {\displaystyle R} denote the smallest index i {\displaystyle i} such that B I T M A P [ i ] = 0 {\displaystyle \mathrm {BITMAP} [i]=0} . Estimate the cardinality of M {\displaystyle M} as 2 R / ϕ {\displaystyle 2^{R}/\phi } , where ϕ ≈ 0.77351 {\displaystyle \phi \approx 0.77351} . The idea is that if n {\displaystyle n} is the number of distinct elements in the multiset M {\displaystyle M} , then B I T M A P [ 0 ] {\displaystyle \mathrm {BITMAP} [0]} is accessed approximately n / 2 {\displaystyle n/2} times, B I T M A P [ 1 ] {\displaystyle \mathrm {BITMAP} [1]} is accessed approximately n / 4 {\displaystyle n/4} times and so on. Consequently, if i ≫ log 2 n {\displaystyle i\gg \log _{2}n} , then B I T M A P [ i ] {\displaystyle \mathrm {BITMAP} [i]} is almost certainly 0, and if i ≪ log 2 n {\displaystyle i\ll \log _{2}n} , then B I T M A P [ i ] {\displaystyle \mathrm {BITMAP} [i]} is almost certainly 1. If i ≈ log 2 n {\displaystyle i\approx \log _{2}n} , then B I T M A P [ i ] {\displaystyle \mathrm {BITMAP} [i]} can be expected to be either 1 or 0. The correction factor ϕ ≈ 0.77351 {\displaystyle \phi \approx 0.77351} (OEIS: A244256) is found by calculations, which can be found in the original article. == Improving accuracy == A problem with the Flajolet–Martin algorithm in the above form is that the results vary significantly. A common solution has been to run the algorithm multiple times with k {\displaystyle k} different hash functions and combine the results from the different runs. One idea is to take the mean of the k {\displaystyle k} results together from each hash function, obtaining a single estimate of the cardinality. The problem with this is that averaging is very susceptible to outliers (which are likely here). A different idea is to use the median, which is less prone to be influences by outliers. The problem with this is that the results can only take form 2 R / ϕ {\displaystyle 2^{R}/\phi } , where R {\displaystyle R} is integer. A common solution is to combine both the mean and the median: Create k ⋅ l {\displaystyle k\cdot l} hash functions and split them into k {\displaystyle k} distinct groups (each of size l {\displaystyle l} ). Within each group use the mean for aggregating together the l {\displaystyle l} results, and finally take the median of the k {\displaystyle k} group estimates as the final estimate. The 2007 HyperLogLog algorithm splits the multiset into subsets and estimates their cardinalities, then it uses the harmonic mean to combine them into an estimate for the original cardinality.
The Algorithm Auction
The Algorithm Auction is the world's first auction of computer algorithms. Created by Ruse Laboratories, the initial auction featured seven lots and was held at the Cooper Hewitt, Smithsonian Design Museum on March 27, 2015. Five lots were physical representations of famous code or algorithms, including a signed, handwritten copy of the original Hello, World! C program by its creator Brian Kernighan on dot-matrix printer paper, a printed copy of 5,000 lines of Assembly code comprising the earliest known version of Turtle Graphics, signed by its creator Hal Abelson, a necktie containing the six-line qrpff algorithm capable of decrypting content on a commercially produced DVD video disc, and a pair of drawings representing OkCupid's original Compatibility Calculation algorithm, signed by the company founders. The qrpff lot sold for $2,500. Two other lots were “living algorithms,” including a set of JavaScript tools for building applications that are accessible to the visually impaired and the other is for a program that converts lines of software code into music. Winning bidders received, along with artifacts related to the algorithms, a full intellectual property license to use, modify, or open-source the code. All lots were sold, with Hello World receiving the most bids. Exhibited alongside the auction lots were a facsimile of the Plimpton 322 tablet on loan from Columbia University, and Nigella, an art-world facing computer virus named after Nigella Lawson and created by cypherpunk and hacktivist Richard Jones. Sebastian Chan, Director of Digital & Emerging Media at the Cooper–Hewitt, attended the event remotely from Milan, Italy via a Beam Pro telepresence robot. == Effects == Following the auction, the Museum of Modern Art held a salon titled The Way of the Algorithm highlighting algorithms as "a ubiquitous and indispensable component of our lives."
Schema crosswalk
A schema crosswalk is a table that shows equivalent elements (or "fields") in more than one database schema. It maps the elements in one schema to the equivalent elements in another. Crosswalk tables are often employed within or in parallel to enterprise systems, especially when multiple systems are interfaced or when the system includes legacy system data. In the context of Interfaces, they function as an internal extract, transform, load (ETL) mechanism. For example, this is a metadata crosswalk from MARC standards to Dublin Core: Crosswalks show people where to put the data from one scheme into a different scheme. They are often used by libraries, archives, museums, and other cultural institutions to translate data to or from MARC standards, Dublin Core, Text Encoding Initiative (TEI), and other metadata schemes. For example, an archive has a MARC record in its catalog describing a manuscript. Suppose the archive makes a digital copy of that manuscript and wants to display it on the web along with the information from the catalog. In that case, it will have to translate the data from the MARC catalog record into a different format, such as Metadata Object Description Schema, that is viewable on a webpage. Because MARC has various fields than MODS, decisions must be made about where to put the data into MODS. This type of "translating" from one format to another is often called "metadata mapping" or "field mapping," and is related to "data mapping", and "semantic mapping". Crosswalks also have several technical capabilities. They help databases using different metadata schemes to share information. They help metadata harvesters create union catalogs. They enable search engines to search multiple databases simultaneously with a single query. == Challenges for crosswalks == One of the biggest challenges for crosswalks is that no two metadata schemes are 100% equivalent. One scheme may have a field that doesn't exist in another scheme or a field that is split into two different fields in another scheme; this is why data is often lost when mapping from a complex scheme to a simpler one. For example, when mapping from MARC to Simple Dublin Core, the distinction between types of titles is lost: Simple Dublin Core only has one "Title" element, so all of the different types of MARC titles get lumped together without further distinctions. A future attempt to convert the metadata back into MARC would enter the information in the basic MARC 245 Title Statement field, with none of the original distinctions. This is why crosswalks are said to be "lateral" (one-way) mappings from one scheme to another. Separate crosswalks would be required to map from scheme A to scheme B and from scheme B to scheme A. === Difficulties in mapping === Other mapping problems arise when: One scheme has one element that needs to be split up with different parts of it placed in multiple other elements in the second scheme ("one-to-many" mapping) One scheme allows an element to be repeated more than once while another only allows that element to appear once with multiple terms in it Schemes have different data formats (e.g. John Doe or Doe, John) An element in one scheme is indexed, but the equivalent element in the other scheme is not Schemes may use different controlled vocabularies Schemes change their standards over time Some of these problems are not fixable. As Karen Coyle says in "Crosswalking Citation Metadata: The University of California's Experience," "The more metadata experience we have, the more it becomes clear that metadata perfection is not attainable, and anyone who attempts it will be sorely disappointed. When metadata is crosswalked between two or more unrelated sources, there will be data elements that cannot be reconciled in an ideal manner. The key to a successful metadata crosswalk is intelligent flexibility. It is essential to focus on the important goals and be willing to compromise to reach a practical conclusion to projects."
Reflection (computer graphics)
Reflection in computer graphics is used to render reflective objects like mirrors and shiny surfaces. Accurate reflections are commonly computed using ray tracing whereas approximate reflections can usually be computed faster by using simpler methods such as environment mapping. Reflections on shiny surfaces like wood or tile can add to the photorealistic effects of a 3D rendering. == Approaches to reflection rendering == For rendering environment reflections there exist many techniques that differ in precision, computational and implementation complexity. Combination of these techniques are also possible. Image order rendering algorithms based on tracing rays of light, such as ray tracing or path tracing, typically compute accurate reflections on general surfaces, including multiple reflections and self reflections. However these algorithms are generally still too computationally expensive for real time rendering (even though specialized HW exists, such as Nvidia RTX) and require a different rendering approach from typically used rasterization. Reflections on planar surfaces, such as planar mirrors or water surfaces, can be computed simply and accurately in real time with two pass rendering — one for the viewer, one for the view in the mirror, usually with the help of stencil buffer. Some older video games used a trick to achieve this effect with one pass rendering by putting the whole mirrored scene behind a transparent plane representing the mirror. Reflections on non-planar (curved) surfaces are more challenging for real time rendering. Main approaches that are used include: Environment mapping (e.g. cube mapping): a technique that has been widely used e.g. in video games, offering reflection approximation that's mostly sufficient to the eye, but lacking self-reflections and requiring pre-rendering of the environment map. The precision can be increased by using a spatial array of environment maps instead of just one. It is also possible to generate cube map reflections in real time, at the cost of memory and computational requirements. Screen space reflections (SSR): a more expensive technique that traces rays come from pixel data.This requires the data of surface normal and either depth buffer (local space) or position buffer (world space).The disadvantage is that objects not captured in the rendered frame cannot appear in the reflections, which results in unresolved and or false intersections causing artefacts such as reflection vanishment and virtual image. SSR was originally introduced as Real Time Local Reflections in CryENGINE 3. == Types of reflection == Polished - A polished reflection is an undisturbed reflection, like a mirror or chrome surface. Blurry - A blurry reflection means that tiny random bumps, or microfacets, on the surface of the material causes the reflection to be blurry. Metallic - A reflection is metallic if the highlights and reflections retain the color of the reflective object. Glossy - This term can be misused: sometimes, it is a setting which is the opposite of blurry (e.g. when "glossiness" has a low value, the reflection is blurry). Sometimes the term is used as a synonym for "blurred reflection". Glossy used in this context means that the reflection is actually blurred. === Polished or mirror reflection === Mirrors are usually almost 100% reflective. === Metallic reflection === Normal (nonmetallic) objects reflect light and colors in the original color of the object being reflected. Metallic objects reflect lights and colors altered by the color of the metallic object itself. === Blurry reflection === Many materials are imperfect reflectors, where the reflections are blurred to various degrees due to surface roughness that scatters the rays of the reflections. === Glossy reflection === Fully glossy reflection, shows highlights from light sources, but does not show a clear reflection from objects. == Examples of reflections == === Wet floor reflections === The wet floor effect is a graphic effects technique popular in conjunction with Web 2.0 style pages, particularly in logos. The effect can be done manually or created with an auxiliary tool which can be installed to create the effect automatically. Unlike a standard computer reflection (and the Java water effect popular in first-generation web graphics), the wet floor effect involves a gradient and often a slant in the reflection, so that the mirrored image appears to be hovering over or resting on a wet floor.
AlphaTensor
AlphaTensor is an artificial intelligence system developed by DeepMind for discovering efficient matrix multiplication algorithms using reinforcement learning. Introduced in 2022, the system was based on AlphaZero and formulated the search for matrix multiplication algorithms as a single-player game called TensorGame. AlphaTensor was designed to search for new ways to multiply matrices with fewer scalar multiplication operations. Matrix multiplication is a fundamental operation in linear algebra, numerical analysis, scientific computing, computer graphics, and machine learning. The system discovered thousands of matrix multiplication algorithms, including algorithms that rediscovered known human-designed methods and others that improved on previously known results for particular matrix sizes and mathematical settings. == Background == Matrix multiplication is one of the basic operations in numerical computing. The standard algorithm for multiplying two square matrices has cubic time complexity, while faster algorithms such as the Strassen algorithm reduce the number of multiplication operations by using more complex algebraic decompositions. Finding optimal matrix multiplication algorithms can be difficult because it involves searching through a large space of possible tensor decompositions. AlphaTensor approached this problem by representing algorithm discovery as TensorGame, in which each move corresponds to an operation that reduces a tensor representing matrix multiplication. The goal of the game is to find a low-rank decomposition of the matrix multiplication tensor, corresponding to an efficient multiplication algorithm. == Development == AlphaTensor was developed by DeepMind and described in a paper published in Nature in October 2022. The system built on the reinforcement-learning approach used in AlphaZero, which had previously been applied to games such as Go, chess, and shogi. Unlike those games, TensorGame involved a very large search space, requiring changes to the AlphaZero-style search method and neural network architecture. DeepMind released source code and discovered algorithms associated with the publication through a public GitHub repository. == Results == AlphaTensor discovered matrix multiplication algorithms over both standard arithmetic and finite fields. One widely reported result was a method for multiplying 4 × 4 matrices over the field with two elements using 47 multiplication operations, improving on the 49 operations required by applying Strassen's algorithm recursively in that setting. The system also found algorithms optimized for particular computer hardware, including algorithms designed for graphics processing units and Tensor Processing Units. DeepMind stated that some of the hardware-specific algorithms improved practical execution time compared with commonly used algorithms on the tested hardware. == Significance == AlphaTensor was described as an example of using machine learning not only to apply existing algorithms, but to assist in discovering new ones. The work was connected to broader research in algorithm discovery, automated machine learning, program synthesis, and computational complexity theory, especially the open problem of determining the optimal complexity of matrix multiplication. AlphaTensor later became part of a broader group of Google DeepMind systems for algorithm and mathematical discovery, alongside systems such as AlphaDev and AlphaEvolve.